Do you want to invent new numbers and new functions? The story of how any age old banking formula led to the discovering of real analysis!
Do you want to invent new numbers and new functions? The story of how any age old banking formula led to the discovering of real analysis!
The golden ratio is arguably the third most interesting number in mathematics. We explore a beautiful problem connecting Number Theory and Geometry.
This is an I.S.I. Entrance Solution Problem: P is a variable point on a circle C and Q is a fixed point on the outside of C. R is a point in PQ dividing it in the ratio p:q, where p> 0 and q > 0 are fixed. Then the locus of R is (A) […]
This is a problem from ISI B.Stat-B.Math Entrance Exam 2018, Subjective Problem 7. It is based on Bases, Exponents and Role reversals. I.S.I. Entrance 2018 Problem 7 Let $(a, b, c)$ are natural numbers such that $(a^{2}+b^{2}=c^{2})$ and $(c-b=1)$. Prove that(i) a is odd.(ii) b is divisible by 4(iii) $( a^{b}+b^{a} )$ is divisible by […]
Pre RMO 2018 Find the problems, discussions and relevant theoretical expositions related to Pre-RMO 2018. Problems of Pre RMO 1. A book is published in three volumes, the pages being numbered from 1 onwards. The page numbers are continued from the first volume to the third. The number of pages in the second volume is […]
Problem Suppose (a, b) are positive real numbers such that (a \sqrt{a}+b \sqrt{b}=183 . a \sqrt{b}+b \sqrt{a}=182). Find (\frac{9}{5}(a+b)). Hint 1 This problem will use the following elementary algebraic identity: $(x+y)^3=x^3+y^3+3 x^2 y+3 x y^2$ Can you identify what is x and what is y? Hint 2 background_video_pause_outside_viewport="on" tab_text_shadow_style="none" body_text_shadow_style="none"] Set $x=\sqrt{a}, y=\sqrt{b}$. Then the […]
In this post we have discussed AMC 10A 2018 problem number 13.
Tools in Geometry is very useful for pre regional mathematical olympiad, regional mathematical olympiad as well as I.S.I. & C.M.I entrance.
Try this beautiful Problem on Fraction from Algebra from AMC 10A, 2015. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 1996, Question 2, based on Greatest Positive Integer.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1993 based on Integers. Use sequential hints if required.
Try this beautiful problem from the PRMO II, 2019, Question 26, based on Distance travelled. You may use sequential hints to solve the problem.
Try this beautiful problem from the PRMO II, 2019 based on the Sum of Digits base 10. You may use sequential hints to solve the problem.
Try this beautiful Problem based on Chords in a Circle, Geometry from PRMO 2017, Question 26. You may use sequential hints to solve the problem.
Try this beautiful Problem from Geometry based on Circle from PRMO 2017, Question 27. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Digits and Rationals.
Try this beautiful problem from Geometry: Side of Square from AMC-10A (2013) Problem 3. You may use sequential hints to solve the problem.
Try this beautiful problem from Algebra based on Counting Days from AMC-10A (2013), Problem 17. You may use sequential hints to solve the problem.